# CAT Ratio and Proportion Questions for CAT Exam with Solutions

Author : Akanksha

Updated On : June 20, 2024

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Overview: If you are a CAT aspirant, you must know that the CAT exam Maths questions are generally tricky and might confuse you with its conceptual questions. CAT Ratio and Proportion questions have been regularly used in over past five years.

The QA section of the CAT exam is generally time-consuming and on the higher side of the difficulty level. In Ratio and Proportion CAT Questions, around 3-4 questions are directly or indirectly related to the basic concepts of this topic. Various shortcut formulas and tricks are used to solve these questions.

This article will answer many questions about profit and loss CAT for rigorous practice. These questions have been carefully selected based on an analysis of past year's trends in the CAT exam.

## Tips Before You Start Solving CAT Ratio and Proportion Questions

The CAT exam preparation requires a strategic approach, especially when tackling CAT Ratio and Proportion questions.

These questions are a staple in the Quantitative Ability section and can be aced with the right techniques. Here are some crucial tips to follow before you start practicing Ratio and Proportion questions for the CAT exam:

#### 1.The Basics of Ratio & Proportion- Before diving into profit and loss CAT questions for practice, ensure you have a solid understanding of the fundamental concepts:

• Ratio: A ratio is a way to compare two quantities by division. Understand how to simplify and interpret ratios.
• Proportion: Proportion refers to the equality of two ratios. Learn how to solve problems involving proportions.

#### 2. Memorize Key Formulas- Familiarize yourself with key formulas and properties related to ratios and proportions:

• The ratio of A to B is expressed as Aor A/B.
• If A= C, then A/B = C/D is a proportion.
• Cross multiplication: If A/B = C/D, then AD = BC.
• Compound ratios: Combine multiple ratios into a single ratio.

Check Now | CAT Exam Analysis

#### 4. Practice Simplification- Get comfortable with simplifying ratios:

• Reduce ratios to their simplest form.
• Convert complex fractions into simpler ratios.

5. Use Varied Practice Sources- Practice CAT Ratio and Proportion questions. questions from various CAT preparation books like Arun Sharma, Nishit Sinha, etc.

6. Analyze Previous Year Papers- Review CAT previous year papers to understand the type and difficulty level of CAT Ratio and Proportion questions that have appeared in the exam. This will give you a better idea of what to expect.

Check | CAT Exam Cut Off Trends

## CAT Ratio and Proportion questions for Practice

1. A tin contains a mixture of Dew and Sprite in the ratio of 7 : 3 and another tin contains the Dew and Sprite in the ratio of 5 : 4. In what proportion should the solution of two tins be mixed to achieve a perfect proportion of 2 : 1 (in which Dew is 2 times that of sprite).

(a) 10: 3
(b) 4 : 1
(c) 3 :10
(d) 3 : 1

2. There are two containers A and B filled with mentha oil with different prices and their volumes are 140 litres and 6 mangoes for a rupee. What is the ratio of profit to the cost price? 60 litres respectively. Equal quantities are drawn from both A and B in such a manner that the oil drawn from A is poured into B and the oil drawn from B is poured into A. The price per litre becomes equal in both A and B. How much oil is drawn from each of A and B :

(a) 40 litre
(b) 21 litre
(c) 42 litre
(d) can’t be determined

3. A three digit number is such that this number itself is divisible by the sum of its digits. The sum of hundreds and unit digit is 6 while the sum of the tens and unit digit is 5. What is the ratio of unit and tens digit :

(a) 1 : 2
(b) 2 : 3
(c) 3 : 4
(d) 2 : 7

Know More | How Many Times CAT Exam is Conducted in a Year

4. Sachin bought 1.5 kg fresh grapes. The ratio of water is to pulp was 4 : 1. When his naughty child crushed these grapes, then some water get wasted. Now the ratio of water is to pulp is 3 : 2. What is the total amount of the crushed grapes?

(a) 0.5 kg
(b) 1 kg
(c) 0.75 kg
(d) none of these

5. A man bought 9 mangoes for a rupee and sold them at 6 mangoes for a rupee.What is the ratio of profit to the cost price?

(a) 3/10
(b) 3/2
(c) 1/2
(d) none of these

6. Half of the volume of Petrol and kerosene mixture of ratio 7 : 5 is converted into a mixture of ratio 3 : 1 by the substitution (or replacement) method. While the mixture of ratio 7 : 5was formed from the mixture of 7 : 3by adding the Kerosene in it. If 240 litres petrol is required in the replacement method, what is the total amount of Kerosene was added to prepare the mixture of 7 : 5 ?

(a) 100 litres
(b) 400 litres
(c) 50 litres
(d) 200 litres

7. Sometimes ago in a Cinema hall a blockbuster movie was being shown. Due to excessive demand of the show, manager of the cinema hall increased the prices of tickets in all the three categories. 25% in first class, 12.5% in special class and 40% in balcony. If the collection of one show was â‚¹ 218925, then find the collection from the balcony only given that the ratio of price of ticket (increased price) for first class, special class and balcony is 5 : 9 : 14 :

(a) 109462.5
(b) 58800
(c) 14400
(d) data insufficient

8. In a mixture of petrol and Kerosene petrol is only 99 litres. if this same quantity of petrol would be presented in another mixture of petrol and Kerosene where total volume would be 198 litres less than the actual mixture then the concentration of petrol in the actual mixture would have been 13.33% point less than that of the new mixture. What is the concentration of petrol in actual mixture?

(a) 20%
(b) 16.66%
(c) 26.66%
(d) 8.33%

9. A drum of 20 litres is filled with milk. A milkman has only two measuring vessels of 3 litres and 5 litres without any calibration. He has to measure four litres of milk for a customer without using any other vessel. Minimum how many operations are required for this work, where an operation is counted if the milk is transferred from one vessel to another vessel?

(a) 5
(b) 6
(c) 8
(d) 11

10. The ages of Vinay, Varsha, Veera and Vikram are in arithmetic progression, but not in order. The ratio of ages of Vinay and Varsha is 6 : 5 and Veera is to Vikram is 7 : 8. Two years later the age of Varsha and Vikram will be 2 : 3. Find the ratio of ages of Vinay and Veera:

(a) 7 : 6
(b) 5 : 8
(c) 6 : 7
(d) 8 : 9

11. A container is filled with the mixture of milk and water. The ratio of milk and water is same. Bobby and Sunny increases the concentration to 60%. Bobby makes it by adding the milk and Sunny makes it by replacing the mixture with milk. What is the percentage of milk added by Bobby to that of milk replaced by Sunny :

(a) 100%
(b) 120%
(c) 133.33%
(d) None of these

12. There are two vessels A and B containing 25 litres each of pure milk and pure water respectively. 5 litres of milk from A is taken and poured into B, then 6 litres of mixture from B is taken and poured in A. What is the ratio of water in A and B respectively:

(a) 4 : 5
(b) 1 : 4
(c) 5 : 4
(d) 2 : 3

13. The ratio of age between A and B is 6 : 5 and the age C and D is 9 times that of B. Age of F is less than A but greater than B. The ratio of ages between B and E is 2 : 3 also age of A is 3 years less than E. What is the ratio of ages of A and F if all the ages are in integers?

(a) 12 : 11
(b) 9 : 7
(c) 24 : 19
(d) 12 : 13

14. The ratio of students in a coaching preparing for B.Tech and MBA is 4 : 5. The ratio of fees collected from each of B. Tech and MBA student is 25 : 16. If the total amount collected from all the students is 1.62 lakh, what is the total amount collected from only MBA aspirants?

(a) â‚¹ 62000
(b) â‚¹ 72000
(c) â‚¹ 80000
(d) none of these

15. The cost of the marble varies directly with square of its weight. Marble is broken into 3 parts whose weights are in the ratio 3 : 4 : 5. If marble had been broken into three equal parts by weight then there would have been a further loss of â‚¹ 1800. What is the actual cost of the original (or unbroken) marble?

(a) â‚¹ 3600
(b) â‚¹ 10800
(c) â‚¹ 2160
(d) none of these

### Conclusion

To have a solid grasp onto Ratio and Proportion questions for CAT exam requires a blend of conceptual understanding, strategic practice, and time management. By practicing the right questions and following the best strategy, you'll be well-prepared to face any Ratio and Proportion questions that come your way.

Ratio and proportion CAT questions require a blend of conceptual understanding and practical application. By mastering these topics, you can enhance your problem-solving skills and perform better in the quantitative section of the CAT exam. Practice diligently and apply the concepts to a variety of problems to build confidence and proficiency. Remember, consistently working on ratio and proportion CAT level questions will not only improve your accuracy but also boost your speed, giving you an edge over other test-takers.

What is the pattern of the CAT exam?

How many questions are there in the CAT exam?

Is there a sectional time limit in the CAT exam?

What types of questions are asked in the DILR section?

Are there negative markings in the CAT exam?

How can I improve my performance in the Quantitative Aptitude section?

# CAT Ratio and Proportion Questions for CAT Exam with Solutions

Author : Akanksha

June 20, 2024

SHARE

Overview: If you are a CAT aspirant, you must know that the CAT exam Maths questions are generally tricky and might confuse you with its conceptual questions. CAT Ratio and Proportion questions have been regularly used in over past five years.

The QA section of the CAT exam is generally time-consuming and on the higher side of the difficulty level. In Ratio and Proportion CAT Questions, around 3-4 questions are directly or indirectly related to the basic concepts of this topic. Various shortcut formulas and tricks are used to solve these questions.

This article will answer many questions about profit and loss CAT for rigorous practice. These questions have been carefully selected based on an analysis of past year's trends in the CAT exam.

## Tips Before You Start Solving CAT Ratio and Proportion Questions

The CAT exam preparation requires a strategic approach, especially when tackling CAT Ratio and Proportion questions.

These questions are a staple in the Quantitative Ability section and can be aced with the right techniques. Here are some crucial tips to follow before you start practicing Ratio and Proportion questions for the CAT exam:

#### 1.The Basics of Ratio & Proportion- Before diving into profit and loss CAT questions for practice, ensure you have a solid understanding of the fundamental concepts:

• Ratio: A ratio is a way to compare two quantities by division. Understand how to simplify and interpret ratios.
• Proportion: Proportion refers to the equality of two ratios. Learn how to solve problems involving proportions.

#### 2. Memorize Key Formulas- Familiarize yourself with key formulas and properties related to ratios and proportions:

• The ratio of A to B is expressed as Aor A/B.
• If A= C, then A/B = C/D is a proportion.
• Cross multiplication: If A/B = C/D, then AD = BC.
• Compound ratios: Combine multiple ratios into a single ratio.

Check Now | CAT Exam Analysis

#### 4. Practice Simplification- Get comfortable with simplifying ratios:

• Reduce ratios to their simplest form.
• Convert complex fractions into simpler ratios.

5. Use Varied Practice Sources- Practice CAT Ratio and Proportion questions. questions from various CAT preparation books like Arun Sharma, Nishit Sinha, etc.

6. Analyze Previous Year Papers- Review CAT previous year papers to understand the type and difficulty level of CAT Ratio and Proportion questions that have appeared in the exam. This will give you a better idea of what to expect.

Check | CAT Exam Cut Off Trends

## CAT Ratio and Proportion questions for Practice

1. A tin contains a mixture of Dew and Sprite in the ratio of 7 : 3 and another tin contains the Dew and Sprite in the ratio of 5 : 4. In what proportion should the solution of two tins be mixed to achieve a perfect proportion of 2 : 1 (in which Dew is 2 times that of sprite).

(a) 10: 3
(b) 4 : 1
(c) 3 :10
(d) 3 : 1

2. There are two containers A and B filled with mentha oil with different prices and their volumes are 140 litres and 6 mangoes for a rupee. What is the ratio of profit to the cost price? 60 litres respectively. Equal quantities are drawn from both A and B in such a manner that the oil drawn from A is poured into B and the oil drawn from B is poured into A. The price per litre becomes equal in both A and B. How much oil is drawn from each of A and B :

(a) 40 litre
(b) 21 litre
(c) 42 litre
(d) can’t be determined

3. A three digit number is such that this number itself is divisible by the sum of its digits. The sum of hundreds and unit digit is 6 while the sum of the tens and unit digit is 5. What is the ratio of unit and tens digit :

(a) 1 : 2
(b) 2 : 3
(c) 3 : 4
(d) 2 : 7

Know More | How Many Times CAT Exam is Conducted in a Year

4. Sachin bought 1.5 kg fresh grapes. The ratio of water is to pulp was 4 : 1. When his naughty child crushed these grapes, then some water get wasted. Now the ratio of water is to pulp is 3 : 2. What is the total amount of the crushed grapes?

(a) 0.5 kg
(b) 1 kg
(c) 0.75 kg
(d) none of these

5. A man bought 9 mangoes for a rupee and sold them at 6 mangoes for a rupee.What is the ratio of profit to the cost price?

(a) 3/10
(b) 3/2
(c) 1/2
(d) none of these

6. Half of the volume of Petrol and kerosene mixture of ratio 7 : 5 is converted into a mixture of ratio 3 : 1 by the substitution (or replacement) method. While the mixture of ratio 7 : 5was formed from the mixture of 7 : 3by adding the Kerosene in it. If 240 litres petrol is required in the replacement method, what is the total amount of Kerosene was added to prepare the mixture of 7 : 5 ?

(a) 100 litres
(b) 400 litres
(c) 50 litres
(d) 200 litres

7. Sometimes ago in a Cinema hall a blockbuster movie was being shown. Due to excessive demand of the show, manager of the cinema hall increased the prices of tickets in all the three categories. 25% in first class, 12.5% in special class and 40% in balcony. If the collection of one show was â‚¹ 218925, then find the collection from the balcony only given that the ratio of price of ticket (increased price) for first class, special class and balcony is 5 : 9 : 14 :

(a) 109462.5
(b) 58800
(c) 14400
(d) data insufficient

8. In a mixture of petrol and Kerosene petrol is only 99 litres. if this same quantity of petrol would be presented in another mixture of petrol and Kerosene where total volume would be 198 litres less than the actual mixture then the concentration of petrol in the actual mixture would have been 13.33% point less than that of the new mixture. What is the concentration of petrol in actual mixture?

(a) 20%
(b) 16.66%
(c) 26.66%
(d) 8.33%

9. A drum of 20 litres is filled with milk. A milkman has only two measuring vessels of 3 litres and 5 litres without any calibration. He has to measure four litres of milk for a customer without using any other vessel. Minimum how many operations are required for this work, where an operation is counted if the milk is transferred from one vessel to another vessel?

(a) 5
(b) 6
(c) 8
(d) 11

10. The ages of Vinay, Varsha, Veera and Vikram are in arithmetic progression, but not in order. The ratio of ages of Vinay and Varsha is 6 : 5 and Veera is to Vikram is 7 : 8. Two years later the age of Varsha and Vikram will be 2 : 3. Find the ratio of ages of Vinay and Veera:

(a) 7 : 6
(b) 5 : 8
(c) 6 : 7
(d) 8 : 9

11. A container is filled with the mixture of milk and water. The ratio of milk and water is same. Bobby and Sunny increases the concentration to 60%. Bobby makes it by adding the milk and Sunny makes it by replacing the mixture with milk. What is the percentage of milk added by Bobby to that of milk replaced by Sunny :

(a) 100%
(b) 120%
(c) 133.33%
(d) None of these

12. There are two vessels A and B containing 25 litres each of pure milk and pure water respectively. 5 litres of milk from A is taken and poured into B, then 6 litres of mixture from B is taken and poured in A. What is the ratio of water in A and B respectively:

(a) 4 : 5
(b) 1 : 4
(c) 5 : 4
(d) 2 : 3

13. The ratio of age between A and B is 6 : 5 and the age C and D is 9 times that of B. Age of F is less than A but greater than B. The ratio of ages between B and E is 2 : 3 also age of A is 3 years less than E. What is the ratio of ages of A and F if all the ages are in integers?

(a) 12 : 11
(b) 9 : 7
(c) 24 : 19
(d) 12 : 13

14. The ratio of students in a coaching preparing for B.Tech and MBA is 4 : 5. The ratio of fees collected from each of B. Tech and MBA student is 25 : 16. If the total amount collected from all the students is 1.62 lakh, what is the total amount collected from only MBA aspirants?

(a) â‚¹ 62000
(b) â‚¹ 72000
(c) â‚¹ 80000
(d) none of these

15. The cost of the marble varies directly with square of its weight. Marble is broken into 3 parts whose weights are in the ratio 3 : 4 : 5. If marble had been broken into three equal parts by weight then there would have been a further loss of â‚¹ 1800. What is the actual cost of the original (or unbroken) marble?

(a) â‚¹ 3600
(b) â‚¹ 10800
(c) â‚¹ 2160
(d) none of these

### Conclusion

To have a solid grasp onto Ratio and Proportion questions for CAT exam requires a blend of conceptual understanding, strategic practice, and time management. By practicing the right questions and following the best strategy, you'll be well-prepared to face any Ratio and Proportion questions that come your way.

Ratio and proportion CAT questions require a blend of conceptual understanding and practical application. By mastering these topics, you can enhance your problem-solving skills and perform better in the quantitative section of the CAT exam. Practice diligently and apply the concepts to a variety of problems to build confidence and proficiency. Remember, consistently working on ratio and proportion CAT level questions will not only improve your accuracy but also boost your speed, giving you an edge over other test-takers.

What is the pattern of the CAT exam?

How many questions are there in the CAT exam?

Is there a sectional time limit in the CAT exam?

What types of questions are asked in the DILR section?

Are there negative markings in the CAT exam?

How can I improve my performance in the Quantitative Aptitude section?

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